M-ary wavelet transform and formulation for perfect reconstructionin M-band filter bank

The binary wavelet transform is generalized and extended to the M-ary biorthonormal case. The computational equivalence between the discrete wavelet analysis and the M-band multirate signal filtering is indicated. The equivalence allows the perfect reconstruction requirement in a filter bank to be investigated from the vector space decomposition/reconstruction in wavelet analysis. From the construction of the biorthonormal wavelet bases, the necessary and sufficient condition for the filters in a perfect reconstruction filter bank is formulated. Under this formulation, an additional optimization procedure is then used to model the frequency domain requirement in filter bank design     

多维多分辨率分析和图像序列的三维子波变换压缩编码

最近有文献报道图像序列的三维子波变换压缩编码。本文讨论了多维多分辨率分析和三维子带系统完全重构的充分必要条件，我们对8帧图像序列进行三级三维子波变换，然后进行零树量化和熵编码，文中给出了不同压缩比下的信噪比。编码器可以在要求的任意压缩比下停止编码．如同图像的二维子波零树编码。     

利用二维非分离型嵌入式子波系数的零树图象编码

本文讨论利用二维非分离型滤渡器组的嵌入式零树子波(Embedded Warder Zerotree，简称EWZ)图象编码。文中讨论了二维非分离型滤波器组完全重构的充要条件，还讨论了子带图象的分割和五点式抽样的问题。实验表明嵌入式零树编码方法可以用在非分离型二维子波变换情况，在低比特率时有很好的巅值信噪比PSNR。     

一种新的二维非线性提升小波变换方法

根据图像的统计信息,本文构造了一种新的非线性算子即统计算子,提出了基于该算子的一种新的非线性提升小波分析方法.使图像经过该方法变换以后,在无量化失真的前提下,以较大概率取得零高频系数.本文将该方法与现存文献中所提出的非线性形态学小波等分析方法,进行了标准图像的测试分析,实验结果显示,利用本文所提出的基于统计算子的提升小波分析的方法所得到的高频子带的熵都低于其它几种非线性小波变换,取得了很好的分析结果.     

一种适于计算声场景分析的混叠语音基音检测方法

本文提出了一种在混叠语音信号中检测各自语音分量基音信息的方法.该方法采用小波变换作为基音检测模型中的滤波处理,并用广义自相关运算突出基音信息,用增强自相关累和消除冗余信息,并提出了用基音概率函数来预测并跟踪不同基音的变化以提高基音检测的准确性.本文提出的方法可应用于计算声场景分析中.实验结果表明,该方法对于混叠语音的基音检测是非常有效的.     

基于正交小波变换的图像去噪算法研究

提出了一种基于正交小波变换的图像去噪方法,首先利用离散小波对图像信号按Mallat算法进行分解,然后采用软闽值与小波重构的算法进行去噪。深入研究了小波变换中的图像分解与重构的Mallat算法,详细介绍了正交小波变换中阈值的选取,并进行了实验研究。实验结果表明,该方法可以有效去除噪声,并保留了图像细节部分的有用信息。     

一种适用于图象去噪的三通道正交完全重建滤波器组

小波变换作为一种多尺度信号分析方法,在图像处理中得到了重要的应用.图像处理的一个重要研究方向就是去噪.由于图像含有大量的边缘,因此用于图像处理的小波基必须具有良好的边缘检测性能和较强的平滑噪声能力.但是,目前还难以找到具有这样特性的正交小波基.本文利用信号的多相位表示理论,提出了一种基于Haar小波的三通道正交完全重建滤波器组,并推导出它在图像去噪中的软门限方法.试验表明,该滤波器组用于图像去噪可以得到很好的结果.     

Progressive medical image coding using binary wavelet transforms

In this paper, a new algorithm for progressive medical image coding is presented. An 8-bit gray scale image is divided into eight binary bit-planes, and then, binary wavelet transform is performed on each bit-plane to extract the three-level multi-resolution binary wavelet transformed images. Starting from the most significant bit-plane, each bit-plane is encoded using quadtree-based partitioning scheme to exploit the energy concentration in the high-frequency subbands. Experiments are conducted on ultrasound, MRI and CT images to prove the effectiveness of the proposed algorithm. The results show a significant improvement in terms of bit-rate for the required peak signal-to-noise ratio and correlation coefficient as compared to the existing state-of-art progressive image coding methods.     

Nonexpansive pyramid for image coding using a nonlinear filterbank

A nonexpansive pyramidal decomposition is proposed for low-complexity image coding. The image is decomposed through a nonlinear filterbank into low- and highpass signals and the recursion of the filterbank over the lowpass signal generates a pyramid resembling that of the octave wavelet transform. The structure itself guarantees perfect reconstruction and we have chosen nonlinear filters for performance reasons. The transformed samples are grouped into square blocks and used to replace the discrete cosine transform (DCT) in the Joint Photographic Expert Group (JPEG) coder. The proposed coder has some advantages over the DCT-based JPEG: computation is greatly reduced, image edges are better encoded, blocking is eliminated, and it allows lossless coding.     

A simple method to build oversampled filter banks and tight frames.

This paper presents conditions under which the sampling lattice for a filter bank can be replaced without loss of perfect reconstruction. This is the generalization of common knowledge that removing up/downsampling will not lose perfect reconstruction. The results provide a simple way of building oversampled filter banks. If the original filter banks are orthogonal, these oversampled banks construct tight frames of l2 (Z(n)) when iterated. As an example, a quincunx lattice is used to replace the rectangular one of the standard wavelet transform. This replacement leads to a tight frame that has a higher sampling in both time and frequency. The frame transform is nearly shift invariant and has intermediate scales. An application of the transform to image fusion is also presented.     

Image reconstruction using the wavelet transform for positronemission tomography

We conducted positron emission tomography (PET) image reconstruction experiments using the wavelet transform. The Wavelet-Vaguelette decomposition was used as a framework from which expressions for the necessary wavelet coefficients might be derived, and then the wavelet shrinkage was applied to the wavelet coefficients for the reconstruction (WVS). The performances of WVS were evaluated and compared with those of the filtered back-projection (FBP) using software phantoms, physical phantoms, and human PET studies. The results demonstrated that WVS gave stable reconstruction over the range of shrinkage parameters and provided better noise and spatial resolution characteristics than FBP.     

基于小波变换和视觉特性的多光谱图像融合

本文提出了一种基于小波变换和人眼视觉系统特性的多光谱图像融合算法。首先对已配准的源图像进行小波多尺度分解;其次基于视觉系统提出一种新的融合规则,即分别将对应的高低频分量分割成若干个块,计算出每个块的对比度方差,通过文中所构造的一种自适应的阈值方法,选取两幅图像中清晰的图像块形成新的高低频分量;最后,通过小波反演变换重构多光谱图像。实验结果表明,这种方法不仅能很好的增强多光谱图像的空间细节能力及光谱信息,而且能避免增强结果出现振铃效应,是一种十分有效的融合方法。     

Two-channel nonseparable wavelets statistically matched to 2-D images

This paper presents a new approach for the estimation of 2-channel nonseparable wavelets matched to images in the statistical sense. To estimate a matched wavelet system, first, we estimate the analysis wavelet filter of a 2-channel nonseparable filterbank using the minimum mean square error (MMSE) criterion. The MMSE criterion requires statistical characterization of the given image. Because wavelet basis expansion behaves as Karhunen-Loève type expansion for fractional Brownian processes, we assume that the given image belongs to a 1st order or a 2nd order isotropic fractional Brownian field (IFBF). Next, we present a method for the design of a 2-channel two-dimensional finite-impulse response (FIR) biorthogonal perfect reconstruction filterbank (PRFB) leading to the estimation of a compactly supported statistically matched wavelet. The important contribution of the paper lies in the fact that all filters are estimated from the given image itself. Several design examples are presented using the proposed theory. Because matched wavelets will have better energy compaction, performance of estimated wavelets is evaluated by computing the transform coding gain. It is seen that nonseparable matched wavelets give better coding gain as compared to nonseparable non-matched orthogonal and biorthogonal wavelets.     

基于稀疏优化的图像压缩感知重建算法

在信号的稀疏表示方法中,传统的基于变换基的稀疏逼近不能自适应性地提取图像的纹理特征,而基于过完备字典的稀疏逼近算法复杂度过高.针对该问题,文章提出了一种基于小波变换稀疏字典优化的图像稀疏表示方法.该算法在图像小波变换的基础上构建图像过完备字典,利用同一场景图像的小波变换在纹理上具有内部和外部相似的属性,对过完备字典进行灰色关联度的分类,有效提高了图像表示的稀疏性.将该新算法应用于图像信号进行稀疏表示,以及基于压缩感知理论的图像采样和重建实验,结果表明新算法总体上提升了重建图像的峰值信噪比与结构相似度,并能有效缩短图像重建时间.     

Turbo encoding and decoding of Reed-Solomon codes through binary decomposition and self-concatenation

This paper presents a two-stage turbo-coding scheme for Reed-Solomon (RS) codes through binary decomposition and self-concatenation. In this scheme, the binary image of an RS code over GF(2/sup m/) is first decomposed into a set of binary component codes with relatively small trellis complexities. Then the RS code is formatted as a self-concatenated code with itself as the outer code and the binary component codes as the inner codes in a turbo-coding arrangement. In decoding, the inner codes are decoded with turbo decoding and the outer code is decoded with either an algebraic decoding algorithm or a reliability-based decoding algorithm. The outer and inner decoders interact during each decoding iteration. For RS codes of lengths up to 255, the proposed two-stage coding scheme is practically implementable and provides a significant coding gain over conventional algebraic and reliability-based decoding algorithms.     

Fresnelets: new multiresolution wavelet bases for digital holography

We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of L/sub 2/ to which we apply a unitary Fresnel transform. The transformed basis functions are shift-invariant on a level-by-level basis but their multiresolution properties are governed by the special form that the dilation operator takes in the Fresnel domain. We derive a Heisenberg-like uncertainty relation that relates the localization of Fresnelets with that of their associated wavelet basis. According to this criterion, the optimal functions for digital hologram processing turn out to be Gabor (1948) functions, bringing together two separate aspects of the holography inventor's work. We give the explicit expression of orthogonal and semi-orthogonal Fresnelet bases corresponding to polynomial spline wavelets. This special choice of Fresnelets is motivated by their near-optimal localization properties and their approximation characteristics. We then present an efficient multiresolution Fresnel transform algorithm, the Fresnelet transform. This algorithm allows for the reconstruction (backpropagation) of complex scalar waves at several user-defined, wavelength-independent resolutions. Furthermore, when reconstructing numerical holograms, the subband decomposition of the Fresnelet transform naturally separates the image to reconstruct from the unwanted zero-order and twin image terms. This greatly facilitates their suppression. We show results of experiments carried out on both synthetic (simulated) data sets as well as on digitally acquired holograms.     

一种自适应整数小波变换方法

本文给出了一种自适应整数小波变换方法。构造整数小波变换的方法通常是由提升结构得到。本文也正是基于一种具有完全重构的自适应提升结构而得到自适应整数小波变换。G.Piella给出的自适应提升结构,由于它严格限制更新步骤中滤波器系数之和为1,使得不易于用它构造整数变换。为了得到整数变换,本文将它推广到更一般的情形。由这种自适应提升结构得到的自适应整数变换对图像中的边缘点和均匀区域有区别地对待,而且对整数信号进行变换没有舍入误差。这些性质在数字图像数据压缩中有重要应用。     

方向扩散方程与小波变换的相关性研究

方向扩散方程是一种有方向性的扩散,本文基于这一特点,对方向扩散方程与小波分解和重构的相关性作了研究。首先,用小波分解后下层的低频图像作为对上层低频图像的一个初始近似,验证了由上层低频图像经方向扩散方程可逐渐扩散收敛到下层的低频图像;反过来,由下层低频图像经方向扩散方程亦可逐渐扩散恢复到上层低频图像,这正体现了小波分解与重构的渐变过程。因此,由方向扩散方程的迭代扩散可以实现小波变换在相邻两层间的分解与重构,且随着所选扩散时间间隔的减小,可以在越来越细的尺度上观察相邻两层间小波分解与重构的渐变过程。     

离散子波提升算法研究及其性能分析

论文基于矩阵变换和变换矩阵级联分解的思想,提出一种新的多相矩阵表示形式,对离散子波提升算法的机理进行了完整的理论分析,对子波提升算法和子波变换双通道滤波实现的理想重构条件进行了等价性证明,并利用互补滤波器组的对偶性提出一利新的子波提升分解算法的级联矩阵分解形式,使提升算法的机理解释更加完善,然后基于文中提出的矩阵级联分解形式,以(2,2)双正交子波变换为例说明了离散子波提升分解算法的实现,并就算法的可逆性、运算量和原位实现等问题进行了简要讨论。